1. Field of the Invention
Example embodiments of the present invention relate to apparatuses and methods of timing recovery. For example, timing recovery apparatuses and/or methods according to one or more example embodiment of the present invention may be used where an input signal has a gain error in a higher noise system and/or when a zero-crossing transition has irregular characteristics.
2. Description of the Related Art
According to the related art, a timing recovery apparatus for determining an initial sampling timing is needed in a receiver of a communication system having lower signal-to-noise ratio (SNR) and/or a read-write head of a mass storage device.
Related art timing recovery apparatuses may use a zero-crossing transition for phase error detection. When using a zero-crossing transition, an arctangent approximation method may be used to approximate a phase compensation value from a phase error value.
FIGS. 1A and 1B are graphs illustrating a related art timing error detection method using the zero-crossing. As shown, a horizontal axis of the graph illustrated in FIG. 1A represents time, and a vertical axis of the graph illustrated in FIG. 1A represents amplitude. In this related art method, an analog input signal may be sampled at expected zero-crossing points in response to a given sampling clock. For example, each input signal may be sampled at every odd numbered sampling point among sampling points having a 90-degree phase interval with respect to one another. The odd numbered sampling points may be represented by the numerals 1, 2, 3 and 4.
In the example illustrated in FIG. 1A, the input signal may be sampled at the expected zero-crossing points, and a timing error may not be detected.
Referring to FIG. 1B, the horizontal axis and the vertical axis of the graph each represent the time and the amplitude of the input signal, respectively, in the same manner as FIG. 1A. As in FIG. 1A, the analog input signal may be sampled at the expected zero-crossing points in response to a given sampling clock. In contrast to FIG. 1A, however, in FIG. 1B the input signal is not sampled at the expected zero-crossing points. That is, for example, at the expected zero-crossing points represented by reference numerals 5, 6, 7 and 8, the input signal is not actually zero. In this case, a phase error is detected.
The phase error may be determined by alternately converting a sign of the input signal value at the sampling points 5, 6, 7 and 8, summing the sampled input signal values and averaging the sum to calculate a quantity of the phase error.
With regard to FIG. 1B, for example, assuming that a sampling value of the input signal sampled at the expected zero-crossing points 5, 6, 7 and 8 is 0.3, −0.3, 0.3 and −0.3, respectively, the phase error is determined based on 0.3, by alternately converting a sign of the 4 sampling values, summing the 4 sampling values, and averaging the sum of the 4 sampling values. In this example, when the average value is a positive value, sampling points may be shifted to the left direction in the time domain. On the other hand, when the average value is a negative value, the sampling points may be shifted to the right direction in the time domain. In either case, the sampling point may be matched to the zero-crossing points at which the value of the input signal is actually zero.
In the related art, the above mentioned arctangent approximation method is used to determine a phase compensation value from the phase error to shift the sampling points collectively along the time axis. The phase compensation value controls a digital clock generator that may generate a sampling clock.
An equation representing the arctangent approximation method may be represented as:tan(θ)=θ  [Equation 1]
As shown in equation 1, the arctangent approximation method may obtain the phase compensation value from the phase error value. For example, the phase compensation value based on the phase error value of 0.3 is approximately 0.3 radians. According to the sign of the phase error value, sampling timing may be increased or decreased.
The approximated phase compensation value according to the arctangent approximation method may be input to a related art digital clock generator, which may generate a sampling clock. A related art digital clock generator may include an oscillator for the sampling clock generation and outputting the sampling clock having the compensated phase in response to the input phase compensation value. As noted above, the output sampling clock may be used to sample the analog input signal.
Conventionally, an initial section of an input signal of a system may include a preamble interval. For example, a preamble interval, such as ‘1100110011001100’, may include two periods of patterns 2-T. This may enable the input signal to maintain a quasi-sine wave in the receiver. As mentioned above, a phase error may be detected by considering the input signal as a sine wave at an expected zero-crossing point based on a sampling value of the input signal in the conventional method.
However, in the related art, the input signal gain may not be considered. Although an automatic gain control (AGC) circuit may control the input signal gain, gain errors may occur. This may result in additional errors due to the gain errors because the conventional arctangent approximation method is carried out at a fixed gain.
In addition, the related art method considers the zero-crossing points to be optimized values and detects the phase error based on the sampled input signals. Channel characteristics of a system are analyzed to cross at zero-crossing points of a preamble interval. However, when the system has non-symmetrical zero-crossing characteristics, other methods may be needed. As such, in the related art, the arctangent approximation method may be applied only when the zero-crossing point is the optimal value.